When \(T_{1}\)  and \(T_{2}\)  are both dual to measured laminations \(\lambda _{1}\)  and \(\lambda _{2}\) , we can actually realize the core \(\mathcal {C}(T_{1}, T_{2})\)  more concretely. Before describing this construction, we need the following result, which can be seen as a special case of the decomposition theorem for general geodesic currents in ([1]}, see also [2]}) about how two measured laminations interact on subsurfaces.
